Dynamical spin Hall conductivity in a disordered two-dimensional system calculated in a self-consistent Born approximation

Physical Review B - Condensed Matter and Materials Physics

Volumn 76, Issue 4, 2007, Pages

  Arii, Katsuyuki ^a   Koshino, Mikito ^a   Ando, Tsuneya ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34447323293     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.76.045311     Document Type: Article

References (56)

1. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science SCIEAS 0036-8075 10.1126/science.1065389 294, 1488 (2001).
2. Semiconductor Spintronics and Quantum Computation, edited by, D. D. Awschalom,,, D. Loss,, and, N. Samarth, (Springer, Berlin, 2002).
3. I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.323 76, 323 (2004).
4. S. Murakami, N. Nagaosa, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1087128 301, 1348 (2003).
5. J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.126603 92, 126603 (2004).
6. J. I. Inoue, G. E. W. Bauer, and L. W. Molenkamp, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.041303 70, 041303 (R) (2004).
7. E. I. Rashba, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.161201 70, 161201 (R) (2004).
8. E. I. Rashba, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.201309 70, 201309 (R) (2004).
9. D. Culcer, J. Sinova, N. A. Sinitsyn, T. Jungwirth, A. H. MacDonald, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.046602 93, 046602 (2004).
10. J. Schliemann and D. Loss, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.165315 69, 165315 (2004).
11. E. G. Mishchenko, A. V. Shytov, and B. I. Halperin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.226602 93, 226602 (2004).
12. R. H. Silsbee, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/16/7/R02 16, R179 (2004).
13. R. Raimondi and P. Schwab, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.033311 71, 033311 (2005).
14. O. Chalaev and D. Loss, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.245318 71, 245318 (2005).
15. O. V. Dimitrova, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.245327 71, 245327 (2005).
16. K. Nomura, J. Sinova, N. A. Sinitsyn, and A. H. MacDonald, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.165316 72, 165316 (2005).
17. V. V. Bryksin and P. Kleinert, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.165313 73, 165313 (2006).
18. A. Khaetskii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96. 056602 96, 056602 (2006).
19. A. V. Shytov, E. G. Mishchenko, H. A. Engel, and B. I. Halperin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.075316 73, 075316 (2006).
20. H.-A. Engel, E. I. Rashba, and B. I. Halperin, Theory of Spin Hall Effects in Semiconductors, in Handbook of Magnetism and Advanced Magnetic Materials Vol. 5 (Wiley, New York, 2007).
21. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science SCIEAS 0036-8075 10.1126/science.1105514 306, 1910 (2004).
22. J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.047204 94, 047204 (2005).
23. V. Sih, R. C. Myers, Y. K. Kato, W. H. Lau, A. C. Gossard, and D. D. Awschalom, Nat. Phys. ZZZZZZ 1745-2473 1, 31 (2005).
24. V. Sih, W. H. Lau, R. C. Myers, V. R. Horowitz, A. C. Gossard, and D. D. Awschalom, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.096605 97, 096605 (2006).
25. N. P. Stern, S. Ghosh, G. Xiang, M. Zhu, N. Samarth, and D. D. Awschalom, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.126603 97, 126603 (2006).
26. F. J. Ohkawa and Y. Uemura, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.37.1325 37, 1325 (1974).
27. Yu. A. Bychkov and E. I. Rashba, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/33/015 17, 6039 (1984).
28. A. Darr, J. P. Kotthaus, and T. Ando, Proceedings of the 13th International Conference on Physics of Semiconductors, Rome, 1976 (Tipographia Marves, Rome, 1976), p. 774.
29. Y. Takada, K. Arai, N. Uchimura, and Y. Uemura, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.49.1851 49, 1851 (1980).
30. T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.54.437 54, 437 (1982), and references cited therein.
31. R. Lassnig, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.8076 31, 8076 (1985).
32. T. Ando, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.5325 40, 5325 (1989).
33. P. Pfeffer and W. Zawadzki, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.R14332 52, R14332 (1995).
34. R. Winkler, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.4245 62, 4245 (2000).
35. W. Zawadzki and P. Pfeffer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.235313 64, 235313 (2001).
36. O. V. Dimitrova, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.245327 71, 245327 (2005).
37. T. Ando and Y. Uemura, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.36.959 36, 959 (1974).
38. T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.36.1521 36, 1521 (1974);
39. T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 37, 622 (1974);
40. T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.37.1233 37, 1233 (1974).
41. J. I. Inoue, G. E. W. Bauer, and L. W. Molenkamp, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.033104 67, 033104 (2003).
42. G. L. Bir and G. E. Pikus, in Symmetry and Strained-Induced Effects in Semiconductors (Wiley, New York, 1974).
43. L. G. Gerchikov and A. V. Subashiev, Sov. Phys. Semicond. SPSEAX 0038-5700 26, 73 (1992).
44. J. Schliemann and D. Loss, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.085308 71, 085308 (2005).
45. S. Y. Liu and X. L. Lei, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.155314 72, 155314 (2005);
46. S. Y. Liu and X. L. Lei, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.249901 72, 249901 (2005).
47. S. Murakami, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.241202 69, 241202 (R) (2004).
48. B. A. Bernevig and S.-C. Zhang, arXiv:cond-mat/0412550 (unpublished).
49. S.-Q. Shen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.081311 70, 081311 (R) (2004).
50. N. A. Sinitsyn, E. M. Hankiewicz, W. Teizer, and J. Sinova, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.081312 70, 081312 (R) (2004).
51. A. G. Malshukov and K. A. Chao, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.121308 71, 121308 (R) (2005).
52. P.-Q. Jin, Y.-Q. Li, and F.-C. Zhang, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/22/022 39, 7115 (2006).
53. S. Murakami, N. Nagaosa, and S.-C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.235206 69, 235206 (2004).
54. S. Zhang and Z. Yang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.066602 94, 066602 (2005).
55. J. Shi, P. Zhang, D. Xiao, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.076604 96, 076604 (2006).
56. N. Sugimoto, S. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.113305 73, 113305 (2006).